a(n) = Sum_{k=1..n} binomial(prime(n),k).

Terms

a(0) =2a(1) =6a(2) =25a(3) =98a(4) =1023a(5) =4095a(6) =41225a(7) =169765a(8) =1698159a(9) =36519555a(10) =160645503a(11) =3231947595a(12) =30273024983a(13) =138712176295